-4/3x+2=3x-11

Solution for -4/3x+2=3x-11 equation:

-4/3x+2=3x-11

We move all terms to the left:

-4/3x+2-(3x-11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-4/3x-3x+11+2=0

We multiply all the terms by the denominator


-3x*3x+11*3x+2*3x-4=0

Wy multiply elements

-9x^2+33x+6x-4=0

We add all the numbers together, and all the variables

-9x^2+39x-4=0

a = -9; b = 39; c = -4;
Δ = b2-4ac
Δ = 392-4·(-9)·(-4)
Δ = 1377
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1377}=\sqrt{81*17}=\sqrt{81}*\sqrt{17}=9\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-9\sqrt{17}}{2*-9}=\frac{-39-9\sqrt{17}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+9\sqrt{17}}{2*-9}=\frac{-39+9\sqrt{17}}{-18}
$